OFFSET
1,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, p. 273.
LINKS
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 33.
Carl Pomerance, The expected number of random elements to generate a finite abelian group, Periodica Mathematica Hungarica 43 (2001), 191-198.
FORMULA
tau = sum_{j >= 1} (1-(1-2^(-j))*prod_{k >= j+1} zeta(k)^(-1)).
tau = sum_{j >= 1} (1-(1-2^(-j))*c*prod_{k = 2..j} zeta(k)), where c is A068982.
EXAMPLE
1.7426523110335154352489048069412986411544379898381...
MATHEMATICA
digits = 101; max = 400; c = 1/Product[N[Zeta[k], digits + 100], {k, 2, max}]; p[j_] := Product[N[Zeta[k], digits + 100], {k, 2, j}]; tau = Sum[1 - (1 - 2^-j)*c*p[j], {j, 1, max}]; RealDigits[tau, 10, digits ] // First
PROG
(PARI) default(realprecision, 120); suminf(j=1, 1-(1-2^(-j))*prodinf(k=j+1, 1/zeta(k))) \\ Vaclav Kotesovec, Oct 22 2014
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Oct 22 2014
STATUS
approved